Determine two pairs of polar coordinates for the point with 0° ≤θ

Question

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°.
-$( 4,4 )$
A) $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$
B) $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$
C) $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$
D) $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point (4,4) in Cartesian coordinates is located in the first quadrant, 45 degrees from the positive x-axis. The distance from the origin is $\sqrt{4^2 + 4^2} = 4\sqrt{2}$, so one set of polar coordinates is $(4\sqrt{2}, 45^\circ)$. For the same point, using a negative radius moves the point to the opposite quadrant (the third quadrant), which is 180 degrees away, giving the coordinates $(-4\sqrt{2}, 225^\circ)$.

Determine Two Pairs of Polar Coordinates for the Point with 0°